Preamble This is actually a question geared towards analytical chemistry, but us analytical chemists are pretty introverted when it comes to on-line forums.  (Doubt me? Check out the Analytical version of VIPEr here. ) Besides, Inorganic chemists are bright, reflective and welcoming, so I'm confident that some of you have thought about this issue or one closely related.

My question boils down to "How truthful should be we to our students?"  (we all know the answer)  We teach propagation of error in both Physical and Analytical Chemistry.  In pchem, we use the standard definition, take the partial derivative of the function with respect to each variable, multiply that by the variable's error and do some squaring and summing.  An important assumption is often overlooked with this method, namely that the variables must be independent.  When performing a measurement such as creating a Beer's Law-style calibration curve to determine an unknown's concentration from its absorbance, the values y, m and b are not independent and and one must include their correlation into the error estimate by utilizing the Variance-Covariance Matrix (for those who are dying to know more, this is a good starting point). 

My problem this; Variance-Covariance matrices (and matrix algebra in general) is tricky for our students (I shall plead the 5th if you ask about my proficiency).  We end up using complicated-looking equations that students don't understand and learning is limited to "if I plug this in AND I don't make a mistake with my parentheses then I'll get the number the professor wants".  I'm attracted to the idea of ignoring the question of independent variables in favor of reinforcing concepts covered in other classes at the expense of exposing students to a subtle, but important aspects of data analysis.  Here's my pros and cons to date:

Pros to teacing error propagation "the pchem way"

• Students see the same error analysis procedure in two different classes.  It reinforces the mathematical concepts and helps students realize that error propagation isn't just a flaming hoop that one professor wants them to jump through.
• Saves valuable lecture/classroom activity time, as I have observed that students can grasp partial derivatives much more readily than matrix alegebra.

Cons

• I'm lying to th students.  The uncertainty they report by the pchem way can be high or low by upwards of 20% (don't quote me on that, it's just what I've observed in a few cases where I've calculated the error both ways).  
• Students shouldn't be afraid of math, and I'm facilitating that fear.

There are analogous "breadth vs. depth" questions in Inorganic Chemistry instruction.  I'd be interested in hearing how you have grappled with such issues and if you've discovered some method, systematic or otherwise, that helped you come to some sort of conclusion.